1. Field of the Invention
The present invention relates to an ultrasonic measuring apparatus for measuring the flow velocity or flow rate of a fluid.
2. Description of the Prior Art
A conventional ultrasonic measuring apparatus provides at least one pair of ultrasonic sensors which are capable of transmitting and receiving an ultrasonic wave through a fluid. The sensors operate alternately as a transmitting sensor and a receiving sensor. An ultrasonic wave is alternately transmitted by an upstream sensor and received by a downstream sensor (hereinafter referred to as "a forward direction") and transmitted by the downstream sensor and received by the upstream sensor (hereinafter referred to as "a reverse direction"). The "upstream" and "downstream" positions are determined with respect to the direction of flow of the fluid being measured. The ultrasonic propagation times are measured and according to the propagation times thus measured the flow rate or flow velocity of the fluid is determined (cf. Japanese Patent Application (OPI) No. 149670/1979, and Japanese Patent Application Publication Nos. 14171/1984 and 14172/1984 for instance).
FIG. 2 is a theoretical diagram of the measurement principle of an ultrasonic measuring apparatus. In FIG. 2 ultrasonic sensors 12a and 12b and wedge members 13a and 13b are placed on or near a pipe 11 through which a fluid 14 flows.
The propagation time of an ultrasonic wave which is transmitted in the forward direction is represented by T.sub.1, and the propagation time of an ultrasonic wave transmitted in the reverse direction is represented by T.sub.2. These propagation times include the periods t.sub.1 and t.sub.2 of propagation of the ultrasonic wave in the fluid. The period .tau.(.tau./2+.tau./2) of propagation in the wedge members 13a and 13b and the pipe 11 can be represented by expressions (1) and (2) as follows: EQU T.sub.1 =t.sub.1 +.tau. (1) EQU T.sub.2 =t.sub.2 +.tau. (2)
The propagation periods t.sub.1 and t.sub.2 in the fluid can be represented by expressions (3) and (4), respectively, as follows: ##EQU1## where C is the sound velocity in the fluid, V is the flow speed, D is the inside diameter of the pipe 11, and .theta. is the ultrasonic propagation angle.
From expressions (3) and (4), the time difference .DELTA.T(=T.sub.2 -T.sub.1) can be obtained as follows: ##EQU2## That is, the time difference .DELTA.T is proportional to the flow velocity V.
Expression (5) includes the sound velocity C in the fluid. The sound velocity C depends on the components or temperature of the fluid. Preferably, therefore, the flow coefficients will not include the sound velocity C. C can be eliminated as follows: If the ultrasonic propagation time in the fluid at rest is represented by T.sub.0, then from expressions (1) and (2) ##EQU3## Expression (6) can be rewritten as follows: ##EQU4## Substitution of expression (7) into expression (5) gives ##EQU5##
The flow rate Q can be represented by the following expression: EQU Q=(sectional area).times.(average flow velocity).
Therefore, from expression (5), the following expression (9) is obtained: ##EQU6## where K is a constant.
When the fluid is at rest, the ultrasonic propagation time is represented by T.sub.0 as described above. However, when the fluid is flowing, the ultrasonic propagation time can be approximated by expression (10) as follows: EQU T.sub.0 =(T.sub.1 +T.sub.2)/2 (10)
This corresponds to the average propagation time.
An ultrasonic wave is refracted when it passes from one medium to another in which the sound velocity is different. Therefore, if the mounting angles of the ultrasonic sensors 12a and 12b are represented by .theta..sub.1, the distance (mounting dimension) between the sensors by L, and angles .theta. and .theta..sub.2, dimensions D, D.sub.1 and L.sub.1 and velocities C.sub.1 and C.sub.2 are as indicated in FIG. 2, then the following relation can be established: ##EQU7## .theta., .theta..sub.2 and L can be represented by expressions (11), (12) and (13), respectively as follows: EQU .theta.=sin.sup.-1 (C/C.sub.1 sin .theta..sub.1) (11) EQU .theta..sub.2 =sin.sup.-1 (C.sub.2 /C.sub.1 sin .theta..sub.1) (12) EQU L=2D.sub.1 tan .theta..sub.2 +D tan .theta. (13)
Therefore, if the inside diameter D of the pipe, the ultrasonic propagation angle .theta. and the propagation period are given, then the flow rate can be obtained from expression (9) by measuring the ultrasonic propagation times T.sub.1 and T.sub.2. In this case, depending on the object to be measured, the pipe inside diameter D is determined, and the propagation time can be represented by the following expression with the data indicated in FIG. 2: ##EQU8## Therefore, the propagation time .tau. can be obtained as a constant if the materials of the pipe and the material of the wedges are determined. As is apparent from expression (11), .theta. is a function of the sound velocity C, and should have a certain value.
The ultrasonic measuring apparatus based on the above-described principle can measure the flow velocity and flow rate of a fluid in a pipe on which the sensors are mounted. Therefore, if a portable ultrasonic measuring apparatus is provided according to the above principles, it can be used to measure flow rates of fluid in pipes.
As described above, an ultrasonic wave signal is applied to the pipe from outside, propagates in the pipe, and is received by the other sensor. In this operation, as is well known in the art, the ultrasonic wave is refracted when passing from one medium to another in which the sound velocity is different, and the angle between the direction of flow and the direction of propagation of the ultrasonic wave, i.e., the ultrasonic propagation angle .theta..sub.1 affects the accuracy of measurement of a flow velocity or flow rate. The angle .theta. further affects the distance L represented by expression (13). Accordingly, in order to improve the accuracy and to accurately detect the received wave, it is essential that the sound velocity C be accurately determined.
As described above, the velocity of an ultrasonic wave in a fluid is dependent upon the type of fluid, the component mixture ratio, the temperature and the pressure of the fluid. Therefore, it is difficult to determine the wave velocity in advance. Thus, the measurement accuracy is reduced, or the types of fluid which can be accurately measured are limited.